Sony Computer Entertainment America has announced that they will begin to shut down the servers for many PS2 and PSP games. The below listed games will all go offline as of June 30th, 2008.
The full list of games is mostly made up of PS2 offerings, with the more popular releases being Jak X, Amplitude, and Twisted Metal Black Online. The only two games which will not work after the servers are shut down include EyeToy Chat and Twisted Metal Black Online due to the fact that they have no offline modes.

The list of PS2 games:
Amplitude
Destruction Derby Arenas
Everybody’s Golf
EyeToy Chat
F1 ‘04
Jak X Combat Racing
Lemmings PS2
My Street
Syphon Filter Omega Strain
This is Football 2004
This is Football 2005
Twisted Metal: Black Online
The list of PSP games:
Lemmings
World Tour Soccer 2
PR via Dbtechno